Is there really going to be that much going on during a coup?!?
First thing to consider, is what are the important points in the city?
In a modern day coup, you grab the centers of communication (TV-station, radio station, & newspaper), as well as securing the support of the local armed forces (police, and any army barracks). (The airforce aren't likely to get involved, bombing civilian targets in their home city isn't popular). Those important police and army personnel that aren't supporting your coup (or at least those that you suspect will actively go against you), you make sure they aren't in town, or seize them. Seizing assets of the local community (courthouse, townhouse) and liberating political prisoners to popularize your efforts also helps. Assassinating people isn't always the best alternative. It always riles people up. You should really only assassinate those diehard followers of the old regime. Preferably through mock trials or through unfortunate "resisting arrest" scenarios. Sending people into exile is usually far more acceptable to other factions as well, and helps getting them onboard.
So for a DnD this translates to:
1) The difficult assumption of seizing the local keep. You'll need well placed supporters for this. Probably the most difficult.
2) Ensuring the support of the local clergy, or making sure they remain passive.
3) Securing the gates/entrances to the city.
4) Propogating a message of peaceful benevolence towards the populance in general, encouraging them to remain calm, and stay indoors during the hours of darkness, until the crisis is over, via bards and town criers.
5) releasing the prisoners from the local jail.
Secondly powerful merchants would be inclined to protest against the sitting government's taxes and levies by closing shop. If they control enough of the trade, they can break the governments coffers by refusing to open for trade (can't tax non-trade), and forment civilian unrest at the same time (compare the bazaariis of Iran in '79), all while blaming the government for the shortage of goods, and the rampant black market.